Balloon-based positioning system and method

ABSTRACT

Disclosed herein are embodiments of a balloon-based positioning system and method. In one example embodiment, a system includes a group of at least three balloons deployed in the stratosphere and a control system configured for: determining a first set of spatial relationships relating to the group; determining a second set of spatial relationships relating to at least a portion of the group and to a reference point; determining a position of the reference point relative to the earth; using the determined first set, the determined second set, and the determined position of the reference point relative to the earth as a basis for determining a position of a target balloon in the group relative to the earth; and transmitting the determined position of the target balloon relative to the earth.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation application of U.S. patentapplication Ser. No. 14/018,153, filed Sep. 4, 2013, which is herebyincorporated by reference in its entirety.

BACKGROUND

Unless otherwise indicated herein, the materials described in thissection are not prior art to the claims in this application and are notadmitted to be prior art by inclusion in this section.

Many positioning systems exist that help determine a position of adevice. One of the most commonly used positioning systems is the GlobalPositioning System (GPS), which is maintained by the United Statesgovernment. The GPS is a satellite-based system that providespositioning information to ground-based receivers located throughout theworld. The GPS include a fleet of thirty-two atomic clock satellites.Each satellite orbits the earth and broadcasts a signal containingsatellite-positioning data for the respective satellite. A givenreceiver then receives signals from different satellites, and processesthe collective satellite-positioning data contained therein as a basisfor determining the receiver's position. However, for a variety ofreasons, the receiver may be unable to receive one or more of thesesignals, or it may receive signals that have been distorted. As aresult, receivers are often unable to accurately determine theirposition. Accordingly, improved positioning systems are desired.

SUMMARY

An example balloon-based positioning system may include a group of atleast three balloons and a control system. Generally, the control systemmay be configured to determine a position of each balloon in the grouprelative to the earth. The control system may make these determinationsbased on one or more spatial relationships, including for example adistance between two balloons or a distance between a balloon and areference point that has a known position relative to the earth. Thecontrol system may then transmit the determined positions to therespective balloons, which in turn may broadcast the determinedpositions such that they may be received and processed by a ground-basedreceiver. This may allow the ground-based receiver to determine itsposition relative to the earth.

In one aspect, a system includes a group of at least three balloonsdeployed in the stratosphere and a control system. The control system isconfigured for: determining a first set of spatial relationshipsrelating to the group; determining a second set of spatial relationshipsrelating to at least a portion of the group and to a reference point;determining a position of the reference point relative to the earth;using the determined first set, the determined second set, and thedetermined position of the reference point relative to the earth as abasis for determining a position of a target balloon in the grouprelative to the earth; and transmitting the determined position of thetarget balloon relative to the earth.

In another aspect, a computer-readable medium has stored thereon programinstructions that upon execution by a processor, cause performance of aset of functions. The set of functions include: determining a first setof spatial relationships relating to a group of at least three balloonsdeployed in the stratosphere; determining a second set of spatialrelationships relating to at least a portion of the group and to areference point; determining a position of the reference point relativeto the earth; using the determined first set, the determined second set,and the determined position of the reference point relative to the earthas a basis for determining a position of a target balloon in the grouprelative to the earth; and transmitting the determined position of thetarget balloon relative to the earth.

In yet another aspect, a method involves: determining, by a computingdevice, a first set of spatial relationships relating to a group of atleast three balloons deployed in the stratosphere, wherein determiningthe first set comprises (i) determining, by the computing device, adistance between a balloon in the group and another balloon in thegroup, and (ii) determining, by the computing device, an angle between afirst vector and a second vector, wherein the first vector extends froma first balloon in the group towards a second balloon in the group, andwherein the second vector extends from the first balloon towards a thirdballoon in the group; determining a second set of spatial relationshipsrelating to at least a portion of the group and to a reference point;determining, by a computing device, a position of the reference pointrelative to the earth; using the determined first set, the determinedsecond set, and the determined position of the reference point relativeto the earth as a basis for determining a position of a target balloonin the group relative to the earth; and transmitting the determinedposition of the target balloon relative to the earth.

In yet another aspect, disclosed are means for: determining a first setof spatial relationships relating to a group of at least three balloonsdeployed in the stratosphere; determining a second set of spatialrelationships relating to at least a portion of the group and to areference point; determining a position of the reference point relativeto the earth; using the determined first set, the determined second set,and the determined position of the reference point relative to the earthas a basis for determining a position of a target balloon in the grouprelative to the earth; and transmitting the determined position of thetarget balloon relative to the earth.

In yet another aspect, disclosed are means for: determining a first setof spatial relationships relating to a group of at least three balloonsdeployed in the stratosphere, wherein determining the first setcomprises (i) determining a distance between a balloon in the group andanother balloon in the group, and (ii) determining an angle between afirst vector and a second vector, wherein the first vector extends froma first balloon in the group towards a second balloon in the group, andwherein the second vector extends from the first balloon towards a thirdballoon in the group; determining a second set of spatial relationshipsrelating to at least a portion of the group and to a reference point;determining a position of the reference point relative to the earth;using the determined first set, the determined second set, and thedetermined position of the reference point relative to the earth as abasis for determining a position of a target balloon in the grouprelative to the earth; and transmitting the determined position of thetarget balloon relative to the earth.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a simplified block diagram illustrating a balloon network,according to an example embodiment.

FIG. 2 is a simplified block diagram illustrating a balloon-networkcontrol system, according to an example embodiment.

FIG. 3 is a simplified block diagram illustrating a high-altitudeballoon, according to an example embodiment.

FIG. 4 is a simplified block diagram illustrating a balloon network thatincludes super-nodes and sub-nodes, according to an example embodiment.

FIG. 5 is a simplified block diagram of a balloon-based positioningsystem, according to an example embodiment.

FIG. 6 is a flow chart showing functions of a method, according to anexample embodiment.

FIG. 7 is an alternate depiction of a portion of the system of FIG. 5.

FIG. 8 is another alternate depiction of a portion of the system of FIG.5.

FIG. 9 is again another alternate depiction of a portion of the systemof FIG. 5.

FIG. 10 is still another alternate depiction of a portion of the systemof FIG. 5.

FIG. 11 is yet another alternate depiction of a portion of the system ofFIG. 5.

FIG. 12 is even another alternate depiction of a portion of the systemof FIG. 5.

DETAILED DESCRIPTION

Throughout this disclosure, unless otherwise specified and/or unless theparticular context clearly dictates otherwise: any usage of “a” or “an”means “at least one,” and any usage of “the” means “the at least one.”

Illustrative embodiments of a balloon-based positioning system aredescribed herein and are not meant to be limiting. Other embodiments maybe utilized, and other changes may be made, without departing from thespirit or scope of the subject matter presented herein. It will bereadily understood that the aspects of the present disclosure, asgenerally described herein, and illustrated in the figures, may bearranged, substituted, combined, separated, and designed in a widevariety of different configurations, all of which are contemplatedherein.

1. Overview

Embodiments of a balloon-based positioning system may be integrated witha balloon data network that includes a plurality of balloons; forexample, a mesh network formed by high-altitude balloons deployed in thestratosphere. Since winds in the stratosphere may affect the positionsof the balloons in a differential manner, each balloon in a network maybe configured to change its horizontal position by adjusting itsvertical position (i.e., altitude). For instance, by adjusting itsaltitude, a balloon may be able find winds that will carry ithorizontally (e.g., latitudinally and/or longitudinally) to a desiredhorizontal location.

In one balloon network, balloons may move latitudinally and/orlongitudinally relative to one another so as to form a desired topology.However, keeping an individual balloon at a specific location may bedifficult due to winds, and possibly for other reasons as well.Accordingly, the desired topology may define a relative framework and/orrules for positioning of balloons relative to one another, such thatballoons can move with respect to the ground, while maintaining thedesired topology. Thus, at a given location on earth, the particularballoon or balloons that provide service may change over time.

In one example, a balloon-based positioning system may include a groupof at least three balloons and a control system. Generally, the controlsystem may be configured to perform one or more functions related todetermining a position of each balloon in the group relative to theearth. The control system may then transmit the determined positions tothe respective balloons, which in turn may broadcast the determinedpositions such that they may be received and processed by a ground-basedreceiver. This may allow the ground-based receiver to determine itsposition relative to the earth.

In one example, the control system may determine the position of eachballoon in the group relative to the earth by determining the positionof each balloon in the group relative to each other balloon in the groupand then determining the position of the group relative to the earth.The control system may make these determinations based on one or morespatial relationships.

A spatial relationship in this context may take a variety of forms. Forexample, a spatial relationship may be a distance between two objects.An object may be a balloon or a reference point that has a knownposition relative to the earth. Such a reference point may be, forexample, a ground-based station, a celestial object, a satellite, orperhaps the earth itself. As another example, a spatial relationship maybe an angle between a first vector and a second vector, where the firstvector extends from a first object towards a second object, and wherethe second vector extends from the first object towards a third object.

In one example, the control system may then use the determined spatialrelationships as constraint-optimization conditions in connection withan optimization function to determine (as an estimate) the position ofeach balloon in the group relative to the earth. The control system mayalso use balloon properties, environmental conditions, and/or other dataas constraint-optimization conditions in this respect. Notably, as thecontrol system considers more observed data, the control system maydetermine the position of each balloon relative to the earth with agreater level of accuracy.

As noted above, once the control system transmits the determinedpositions to the respective balloons, the balloons may broadcast theirrespective positions. In one example, each balloon may include aposition-broadcasting module (PBM) configured for broadcasting a balloonsignal containing balloon-positioning data. The balloon-positioning datamay include the position of the respective balloon and a correspondingtime of broadcast (i.e., indicating when the balloon signal wasbroadcast). These balloon signals may then be used by a ground-basedreceiver as a basis for determining its position relative to the earth.As such, the ground-based receiver may be configured to receive theseballoon signals and determine its position based on the collectiveballoon-positioning data contained therein, such as by employing atriangulation technique.

Embodiments of a balloon-based positioning system may provide severaladvantages. As one example, the typical distance from a balloon to aground-based receiver is relatively short, as compared to for example,the typical distance from a GPS satellite to a ground-based receiver. Asa result, balloon signals are likely to be stronger, and are more likelyto reach ground-based receivers, as compared to in a parallel GPSscenario.

As another example advantage, the balloons are positioned beneath theionosphere. As a result, the balloon signals need not traverse theionosphere to reach ground-based receivers, and therefore they may avoidrefraction-based interference that is caused by the ionosphere. Again,this means that balloon signals are likely to be stronger, and are morelikely to reach ground-based receivers, as compared to in a parallel GPSscenario where satellite signals traverse the ionosphere.

Notably, to minimize the effects of refraction-based interference,satellite signals are typically broadcast simultaneously on twodifferent channel frequencies. Since balloon signals avoid this type ofinterference, they may be broadcast on a single channel frequency. Amongother things, this may allow ground-based receivers to be less complex,as compared to those used in the GPS that must be configured to receivesignals on multiple channels.

While not necessary, some embodiments of a balloon-based positioningsystem may include a large number of balloons, including thousands, tensof thousands, or more. In addition to providing additional data fordetermining more spatial relationships, these embodiments provide afurther advantage of increasing the likelihood that a given ground-basedreceiver will have a direct line-of-sight with one or more of theballoons. Accordingly, balloon signals are more likely to reachground-based receivers, as compared to in a parallel GPS scenario wherethe GPS is limited by its fleet of thirty-two satellites.

It should be appreciated that the possible benefits and advantagesdescribed above are merely examples and are non-limiting. Embodiments ofa balloon-based positioning system may provide additional advantages,such as those described in greater detail throughout this disclosure,and/or those that would be apparent to one of ordinary skill in the art.Further, the possible benefits and advantages described are notnecessarily required, and should not be construed as limiting theclaims.

2. Example Balloon Networks

In some embodiments, a high-altitude-balloon network may be homogenous.That is, the balloons in a high-altitude-balloon network could besubstantially similar to each other in one or more ways. Morespecifically, in a homogenous high-altitude-balloon network, eachballoon is configured to communicate with nearby balloons via free-spaceoptical links. Further, some or all of the balloons in such a network,may also be configured to communicate with ground-based station(s) usingRF communications. (Note that in some embodiments, the balloons may behomogenous in so far as each balloon is configured for free-spaceoptical communication with other balloons, but heterogeneous with regardto RF communications with ground-based stations.)

In other embodiments, a high-altitude-balloon network may beheterogeneous, and thus may include two or more different types ofballoons. For example, some balloons may be configured as super-nodes,while other balloons may be configured as sub-nodes. Some balloons maybe configured to function as both a super-node and a sub-node. Suchballoons may function as either a super-node or a sub-node at aparticular time, or, alternatively, act as both simultaneously dependingon the context. For instance, an example balloon could aggregate searchrequests of a first type to transmit to a ground-based station. Theexample balloon could also send search requests of a second type toanother balloon, which could act as a super-node in that context.

In such a configuration, the super-node balloons may be configured tocommunicate with nearby super-node balloons via free-space opticallinks. However, the sub-node balloons may not be configured forfree-space optical communication, and may instead be configured for someother type of communication, such as RF communications. In that case, asuper-node may be further configured to communicate with sub-nodes usingRF communications. Thus, the sub-nodes may relay communications betweenthe super-nodes and one or more ground-based stations using RFcommunications. In this way, the super-nodes may collectively functionas backhaul for the balloon network, while the sub-nodes function torelay communications from the super-nodes to ground-based stations.Other differences could be present between balloons in a heterogeneousballoon network.

FIG. 1 is a simplified block diagram illustrating a balloon network 100,according to an example embodiment. As shown, balloon network 100includes balloons 102A to 102F, which are configured to communicate withone another via free-space optical links 104. Balloons 102A to 102Fcould additionally or alternatively be configured to communicate withone another via RF links 114. Balloons 102A to 102F may collectivelyfunction as a mesh network for packet-data communications. Further,balloons 102A to 102F may be configured for RF communications withground-based stations 106 and 112 via RF links 108. In another exampleembodiment, balloons 102A to 102F could be configured to communicate viaoptical link 110 with ground-based station 112.

In an example embodiment, balloons 102A to 102F are high-altitudeballoons, which are deployed in the stratosphere. At moderate latitudes,the stratosphere includes altitudes between approximately 10 kilometers(km) and 50 km altitude above the surface. At the poles, thestratosphere starts at an altitude of approximately 8 km. In an exampleembodiment, high-altitude balloons may be generally configured tooperate in an altitude range within the stratosphere that has lowerwinds (e.g., between 5 and 20 miles per hour (mph)).

More specifically, in a high-altitude-balloon network, balloons 102A to102F may generally be configured to operate at altitudes between 17 kmand 25 km (although other altitudes are possible). This altitude rangemay be advantageous for several reasons. In particular, this layer ofthe stratosphere generally has mild wind and turbulence (e.g., windsbetween 5 and 20 miles per hour (mph)). Further, while the winds between17 km and 25 km may vary with latitude and by season, the variations canbe modeled in a reasonably accurate manner. Additionally, altitudesabove 17 km are typically above the maximum flight level designated forcommercial air traffic. Therefore, interference with commercial flightsis not a concern when balloons are deployed between 17 km and 25 km.Additional advantages relating to this altitude range, particularly inconnection with positioning-related features, are discussed in greaterdetail below.

To transmit data to another balloon, a given balloon 102A to 102F may beconfigured to transmit an optical signal via an optical link 104. In anexample embodiment, a given balloon 102A to 102F may use one or morehigh-power light-emitting diodes (LEDs) to transmit an optical signal.Alternatively, some or all of balloons 102A to 102F may include lasersystems for free-space optical communications over optical links 104.Other types of free-space optical communication are possible. Further,in order to receive an optical signal from another balloon via anoptical link 104, a given balloon 102A to 102F may include one or moreoptical receivers. Additional details of example balloons are discussedin greater detail below, with reference to FIG. 3.

In a further aspect, balloons 102A to 102F may utilize one or more ofvarious different RF air-interface protocols for communication withground-based stations 106 and 112 via RF links 108. For instance, someor all of balloons 102A to 102F may be configured to communicate withground-based stations 106 and 112 using protocols described in IEEE802.11 (including any of the IEEE 802.11 revisions), various cellularprotocols such as GSM, CDMA, UMTS, EV-DO, WiMAX, and/or LTE, and/or oneor more propriety protocols developed for balloon-to-ground RFcommunication, among other possibilities.

In a further aspect, there may be scenarios where RF links 108 do notprovide a desired link capacity for balloon-to-ground communications.For instance, increased capacity may be desirable to provide backhaullinks from a ground-based gateway, and in other scenarios as well.Accordingly, an example network may also include downlink balloons,which could provide a high-capacity air-ground link.

For example, in balloon network 100, balloon 102F could be configured asa downlink balloon. Like other balloons in an example network, adownlink balloon 102F may be operable for optical communication withother balloons via optical links 104. However, downlink balloon 102F mayalso be configured for free-space optical communication with aground-based station 112 via an optical link 110. Optical link 110 maytherefore serve as a high-capacity link (as compared to an RF link 108)between the balloon network 100 and a ground-based station 112.

Note that in some implementations, a downlink balloon 102F mayadditionally be operable for RF communication with ground-based stations106. In other cases, a downlink balloon 102F may only use an opticallink for balloon-to-ground communications. Further, while thearrangement shown in FIG. 1 includes just one downlink balloon 102F, anexample balloon network can also include multiple downlink balloons. Onthe other hand, a balloon network can also be implemented without anydownlink balloons.

In other implementations, a downlink balloon may be equipped with aspecialized, high-bandwidth RF communication system forballoon-to-ground communications, instead of, or in addition to, afree-space optical communication system. The high-bandwidth RFcommunication system may take the form of an ultra-wideband system,which provides an RF link with substantially the same capacity as theoptical links 104. Other forms are also possible.

Balloons could be configured to establish a communication link withspace-based satellites in addition to, or as an alternative to, aground-based communication link.

Ground-based stations, such as ground-based stations 106 and/or 112, maytake various forms. Generally, a ground-based station may includecomponents such as transceivers, transmitters, and/or receivers forcommunication via RF links and/or optical links with a balloon network.Further, a ground-based station may use various air-interface protocolsin order communicate with a balloon 102A to 102F over an RF link 108. Assuch, ground-based stations 106 and 112 may be configured as an accesspoint with which various devices can connect to balloon network 100.Ground-based stations 106 and 112 may have other configurations and/orserve other purposes without departing from the scope of the invention.

Further, some ground-based stations, such as ground-based stations 106and 112, may be configured as gateways between balloon network 100 andone or more other networks. Such ground-based stations 106 and 112 maythus serve as an interface between the balloon network and the Internet,a cellular service provider's network, and/or other types of networks.Variations on this configuration and other configurations ofground-based stations 106 and 112 are also possible.

2a) Mesh Network Functionality

As noted, balloons 102A to 102F may collectively function as a meshnetwork. More specifically, since balloons 102A to 102F may communicatewith one another using free-space optical links, the balloons maycollectively function as a free-space optical mesh network.

In a mesh-network configuration, each balloon 102A to 102F may functionas a node of the mesh network, which is operable to receive datadirected to it and to route data to other balloons. As such, data may berouted from a source balloon to a destination balloon by determining anappropriate sequence of optical links between the source balloon and thedestination balloon. These optical links may be collectively referred toas a “lightpath” for the connection between the source and destinationballoons. Further, each of the optical links may be referred to as a“hop” on the lightpath.

To operate as a mesh network, balloons 102A to 102F may employ variousrouting techniques and self-healing algorithms. In some embodiments, aballoon network 100 may employ adaptive or dynamic routing, where alightpath between a source and destination balloon is determined andset-up when the connection is needed, and released at a later time.Further, when adaptive routing is used, the lightpath may be determineddynamically depending upon the current state, past state, and/orpredicted state of the balloon network.

In addition, the network topology may change as the balloons 102A to102F move relative to one another and/or relative to the ground.Accordingly, an example balloon network 100 may apply a mesh protocol toupdate the state of the network as the topology of the network changes.For example, to address the mobility of the balloons 102A to 102F,balloon network 100 may employ and/or adapt various techniques that areemployed in mobile ad hoc networks (MANETs). Other examples are possibleas well.

In some implementations, a balloon network 100 may be configured as atransparent mesh network. More specifically, in a transparent balloonnetwork, the balloons may include components for physical switching thatis entirely optical, without any electrical operations involved inphysical routing of optical signals. Thus, in a transparentconfiguration with optical switching, signals travel through a multi-hoplightpath that is entirely optical.

In other implementations, the balloon network 100 may implement afree-space optical mesh network that is opaque. In an opaqueconfiguration, some or all balloons 102A to 102F may implementoptical-electrical-optical (OEO) switching. For example, some or allballoons may include optical cross-connects (OXCs) for OEO conversion ofoptical signals. Other opaque configurations are also possible.Additionally, network configurations are possible that include routingpaths with both transparent and opaque sections.

In a further aspect, balloons in an example balloon network 100 mayimplement wavelength division multiplexing (WDM), which may help toincrease link capacity. When WDM is implemented with transparentswitching, physical lightpaths through the balloon network may besubject to the “wavelength continuity constraint.” More specifically,because the switching in a transparent network is entirely optical, itmay be necessary to assign the same wavelength for all optical links ona given lightpath.

An opaque configuration, on the other hand, may avoid the wavelengthcontinuity constraint. In particular, balloons in an opaque balloonnetwork may include the OEO switching systems operable for wavelengthconversion. As a result, balloons can convert the wavelength of anoptical signal at each hop along a lightpath. Alternatively, opticalwavelength conversion could take place at only selected hops along thelightpath.

Further, various routing algorithms may be employed in an opaqueconfiguration. For example, to determine a primary lightpath and/or oneor more diverse backup lightpaths for a given connection, exampleballoons may apply or consider shortest-path routing techniques such asDijkstra's algorithm and k-shortest path, and/or edge and node-diverseor disjoint routing such as Suurballe's algorithm, among others.Additionally or alternatively, techniques for maintaining a particularQuality of Service (QoS) may be employed when determining a lightpath.Other techniques are also possible.

2b) Station-Keeping Functionality

In one embodiment, a balloon network 100 may implement station-keepingfunctions to help provide a desired network topology. For example,station-keeping may involve each balloon 102A to 102F maintaining and/ormoving into a certain position relative to one or more other balloons inthe network (and possibly in a certain position relative to the ground).As part of this process, each balloon 102A to 102F may implementstation-keeping functions to determine its desired positioning withinthe desired topology, and if necessary, to determine how to move to thedesired position.

The desired topology may vary depending upon the particularimplementation. In some cases, balloons may implement station-keeping toprovide a substantially uniform topology. In such cases, a given balloon102A to 102F may implement station-keeping functions to position itselfat substantially the same distance (or within a certain range ofdistances) from adjacent balloons in the balloon network 100.

In other cases, a balloon network 100 may have a non-uniform topology.For instance, example embodiments may involve topologies where balloonsare distributed more or less densely in certain areas, for variousreasons. As an example, to help meet the higher bandwidth demands thatare typical in urban areas, balloons may be clustered more densely overurban areas. For similar reasons, the distribution of balloons may bedenser over land than over large bodies of water. Many other examples ofnon-uniform topologies are possible.

In a further aspect, the topology of an example balloon network may beadaptable. In particular, station-keeping functionality of exampleballoons may allow the balloons to adjust their respective positioningin accordance with a change in the desired topology of the network. Forexample, one or more balloons could move to new positions to increase ordecrease the density of balloons in a given area. Other examples arepossible.

In some embodiments, a balloon network 100 may employ an energy functionto determine if and/or how balloons should move to provide a desiredtopology. In particular, the state of a given balloon and the states ofsome or all nearby balloons may be input to an energy function. Theenergy function may apply the current states of the given balloon andthe nearby balloons to a desired network state (e.g., a statecorresponding to the desired topology). A vector indicating a desiredmovement of the given balloon may then be determined by determining thegradient of the energy function. The given balloon may then determineappropriate actions to take in order to effectuate the desired movement.For example, a balloon may determine an altitude adjustment oradjustments such that winds will move the balloon in the desired manner.

2c) Control of Balloons in a Balloon Network

In some embodiments, mesh networking and/or station-keeping functionsmay be centralized. For example, FIG. 2 is a block diagram illustratinga balloon-network control system, according to an example embodiment. Inparticular, FIG. 2 shows a distributed control system, which includes acentral control system 200 and a number of regional control-systems 202Ato 202B. Such a control system may be configured to coordinate certainfunctionality for balloon network 204, and as such, may be configured tocontrol and/or coordinate certain functions for balloons 206A to 206I.

In the illustrated embodiment, central control system 200 may beconfigured to communicate with balloons 206A to 206I via a number ofregional control systems 202A to 202C. These regional control systems202A to 202C may be configured to receive communications and/oraggregate data from balloons in the respective geographic areas thatthey cover, and to relay the communications and/or data to centralcontrol system 200. Further, regional control systems 202A to 202C maybe configured to route communications from central control system 200 tothe balloons in their respective geographic areas. For instance, asshown in FIG. 2, regional control system 202A may relay communicationsand/or data between balloons 206A to 206C and central control system200, regional control system 202B may relay communications and/or databetween balloons 206D to 206F and central control system 200, andregional control system 202C may relay communications and/or databetween balloons 206G to 206I and central control system 200.

In order to facilitate communications between the central control system200 and balloons 206A to 206I, certain balloons may be configured asdownlink balloons, which are operable to communicate with regionalcontrol systems 202A to 202C. Accordingly, each regional control system202A to 202C may be configured to communicate with the downlink balloonor balloons in the respective geographic area it covers. For example, inthe illustrated embodiment, balloons 206A, 206F, and 206I are configuredas downlink balloons. As such, regional control systems 202A to 202C mayrespectively communicate with balloons 206A, 206F, and 206I via opticallinks 208, 210, and 212, respectively.

In the illustrated configuration, where only some of balloons 206A to206I are configured as downlink balloons, the balloons 206A, 206F, and206I that are configured as downlink balloons may function to relaycommunications from central control system 200 to other balloons in theballoon network, such as balloons 206B to 206E, 206G, and 206H. However,it should be understood that it in some implementations, it is possiblethat all balloons may function as downlink balloons. Further, while FIG.2 shows multiple balloons configured as downlink balloons, it is alsopossible for a balloon network to include only one downlink balloon.

Note that a regional control system 202A to 202C may in fact just be aparticular type of ground-based station that is configured tocommunicate with downlink balloons (e.g. the ground-based station 112 ofFIG. 1). Thus, while not shown in FIG. 2, a control system may beimplemented in conjunction with other types of ground-based stations(e.g., access points, gateways, etc.).

In a centralized control arrangement, such as that shown in FIG. 2, thecentral control system 200 (and possibly regional control systems 202Ato 202C as well) may coordinate certain mesh-networking functions forballoon network 204. For example, balloons 206A to 206I may send thecentral control system 200 certain state information, which the centralcontrol system 200 may utilize to determine the state of balloon network204. The state information from a given balloon may include positiondata, optical-link information (e.g., the identity of other balloonswith which the balloon has established an optical link, the bandwidth ofthe link, wavelength usage and/or availability on a link, etc.), winddata collected by the balloon, and/or other types of information.Accordingly, the central control system 200 may aggregate stateinformation from some or all the balloons 206A to 206I in order todetermine an overall state of the network.

The overall state of the network may then be used to coordinate and/orfacilitate certain mesh-networking functions such as determininglightpaths for connections. For example, the central control system 200may determine a current topology based on the aggregate stateinformation from some or all the balloons 206A to 206I. The topology mayprovide a picture of the current optical links that are available in theballoon network and/or the wavelength availability on the links. Thistopology may then be sent to some or all of the balloons so that arouting technique may be employed to select appropriate lightpaths (andpossibly backup lightpaths) for communications through the balloonnetwork 204.

In a further aspect, the central control system 200 (and possiblyregional control systems 202A to 202C as well) may also coordinatecertain station-keeping functions for balloon network 204. For example,the central control system 200 may input state information that isreceived from balloons 206A to 206I to an energy function, which mayeffectively compare the current topology of the network to a desiredtopology, and provide a vector indicating a direction of movement (ifany) for each balloon, such that the balloons can move towards thedesired topology. Further, the central control system 200 may usealtitudinal wind data to determine respective altitude adjustments thatmay be initiated to achieve the movement towards the desired topology.The central control system 200 may provide and/or support otherstation-keeping functions as well.

FIG. 2 shows a distributed arrangement that provides centralizedcontrol, with regional control systems 202A to 202C coordinatingcommunications between a central control system 200 and a balloonnetwork 204. Such an arrangement may be useful to provide centralizedcontrol for a balloon network that covers a large geographic area. Insome embodiments, a distributed arrangement may even support a globalballoon network that provides coverage everywhere on earth. Adistributed-control arrangement may be useful in other scenarios aswell.

Further, it should be understood that other control-system arrangementsare possible. For instance, some implementations may involve acentralized control system with additional layers (e.g., sub-regionsystems within the regional control systems, and so on). Alternatively,control functions may be provided by a single, centralized, controlsystem, which communicates directly with one or more downlink balloons.

In some embodiments, control and coordination of a balloon network maybe shared between a ground-based control system and a balloon network tovarying degrees, depending upon the implementation. In fact, in someembodiments, there may be no ground-based control systems. In such anembodiment, all network control and coordination functions may beimplemented by the balloon network itself. For example, certain balloonsmay be configured to provide the same or similar functions as centralcontrol system 200 and/or regional control systems 202A to 202C. Otherexamples are also possible.

Furthermore, control and/or coordination of a balloon network may bede-centralized. For example, each balloon may relay state informationto, and receive state information from, some or all nearby balloons.Further, each balloon may relay state information that it receives froma nearby balloon to some or all nearby balloons. When all balloons doso, each balloon may be able to individually determine the state of thenetwork. Alternatively, certain balloons may be designated to aggregatestate information for a given portion of the network. These balloons maythen coordinate with one another to determine the overall state of thenetwork.

Further, in some aspects, control of a balloon network may be partiallyor entirely localized, such that it is not dependent on the overallstate of the network. For example, individual balloons may implementstation-keeping functions that only consider nearby balloons. Inparticular, each balloon may implement an energy function that takesinto account its own state and the states of nearby balloons. The energyfunction may be used to maintain and/or move to a desired position withrespect to the nearby balloons, without necessarily considering thedesired topology of the network as a whole. However, when each balloonimplements such an energy function for station-keeping, the balloonnetwork as a whole may maintain and/or move towards the desiredtopology.

As an example, each balloon A may receive distance information d₁ tod_(k) with respect to each of its k closest neighbors. Each balloon Amay treat the distance to each of the k balloons as a virtual springwith a vector representing a force direction from the first nearestneighbor balloon i toward balloon A and with force magnitudeproportional to d_(i). The balloon A may sum each of the k vectors andthe summed vector is the vector of desired movement for balloon A.Balloon A may attempt to achieve the desired movement by controlling itsaltitude.

Alternatively, this process could assign the force magnitude of each ofthese virtual forces equal to d_(i)×d_(I), wherein d_(I) is proportionalto the distance to the second nearest neighbor balloon, for instance.

In another embodiment, a similar process could be carried out for eachof the k balloons and each balloon could transmit its planned movementvector to its local neighbors. Further rounds of refinement to eachballoon's planned movement vector can be made based on the correspondingplanned movement vectors of its neighbors. It will be evident to thoseskilled in the art that other algorithms could be implemented in aballoon network in an effort to maintain a set of balloon spacingsand/or a specific network capacity level over a given geographiclocation.

2d) Example Balloon Configuration

Various types of balloons may be incorporated in an example balloonnetwork. As noted above, an example embodiment may utilize high-altitudeballoons, which could typically operate in an altitude range between 17km and 25 km. FIG. 3 shows a high-altitude balloon 300, according to anexample embodiment. As shown, the balloon 300 includes an envelope 302,a skirt 304, a payload 306, and a cut-down system 308, which is attachedbetween the balloon 302 and payload 304.

The envelope 302 and skirt 304 may take various forms, which may becurrently well-known or yet to be developed. For instance, the envelope302 and/or skirt 304 may be made of a highly-flexible latex material ormay be made of a rubber material such as chloroprene. In one exampleembodiment, the envelope and/or skirt could be made of metalized Mylaror BoPet. Other materials are also possible. Further, the shape and sizeof the envelope 302 and skirt 304 may vary depending upon the particularimplementation. Additionally, the envelope 302 may be filled withvarious different types of gases, such as helium and/or hydrogen. Othertypes of gases are possible as well.

The payload 306 of balloon 300 may include a processor 312 and on-boarddata storage, such as memory 314. The memory 314 may take the form of orinclude a non-transitory computer-readable medium. The non-transitorycomputer-readable medium may have instructions stored thereon, which canbe accessed and executed by the processor 312 in order to carry out theballoon functions described herein.

The payload 306 of balloon 300 may also include various other types ofequipment and systems to provide a number of different functions. Forexample, payload 306 may include optical communication system 316, whichmay transmit optical signals via an optical signal transmitter (e.g., anultra-bright LED transmitter) 320, and which may receive optical signalsvia an optical signal receiver 322 (e.g., a photodiode receiver). In oneexample, the optical signal transmitter 320 may be configured totransmit optical signals (using a modulation technique) in amultidirectional or omnidirectional manner. Similarly, the opticalsignal receiver 322 may be configured to receive optical signals from avariety of different directions at a given time.

In some instances, the optical signal transmitter may take the form of asteerable optical signal transmitter (referred to herein as a “steerabletransmitter”) and the optical signal receiver may take the form of asteerable optical signal receiver (referred to herein as a “steerablereceiver”). In one example, the steerable transmitter and steerablereceiver may be integrated together as a steerable transmitter/receiver344. The steerable transmitter may be configured to transmit opticalsignals in a relatively focused manner, as compared to themultidirectional or omnidirectional manners discussed above. Similarly,the steerable receiver may be configured to receive optical signals froma relatively focused direction, as compared to from a variety ofdifferent directions as discussed above.

The steerable transmitter/receiver 344 (or the steerable transmitterand/or the steerable receiver individually) may be configured to rotateabout one or more axes (e.g., defining yaw and pitch Euler angleoffsets). This may allow two balloons to steer their respectivesteerable transmitter/receiver towards each other such that therespective balloons may communicate using free-space optical links. Insome instances, alignment techniques may be used to properly orient eachsteerable transmitter/receiver. Further, the combined use of a steerabletransmitter on one balloon and an optical signal receiver on anotherballoon may aid in determining a particular angle-based spatialrelationship as described in greater detail below.

Notably, the optical communication system 316 may be implemented invarious ways (e.g., with mechanical systems and/or with hardware,firmware, and/or software) depending upon the particular application.

The payload 306 may also include a reflector (sometimes called aretro-reflector) 346 that is configured to reflect (in one or moredirections) an optical signal directed at it. The combined use of asteerable transmitter on one balloon and a reflector on another balloonmay also aid in determining a particular angle-based spatialrelationship as described in greater detail below.

Payload 306 may also include an RF communication system 318, which maytransmit and/or receive RF communications via an antenna system 340. Theoptical communication system 316 and/or the RF communication system 318are examples of communication systems that may include communicationinterfaces for communications between a balloon and other nodes in aballoon network. It should be understood that other types ofcommunication systems that provide other types of communicationinterfaces are also possible, and may vary depending upon the particularnetwork implementation.

The payload 306 may also include a power supply 326 to supply power tothe various components of balloon 300. The power supply 326 couldinclude a rechargeable battery. In other embodiments, the power supply326 may additionally or alternatively represent other means known in theart for producing power. In addition, the balloon 300 may include asolar power generation system 327. The solar power generation system 327may include solar panels and could be used to generate power thatcharges and/or is distributed by power supply 326.

Further, payload 306 may include various types of other systems andsensors 328 managed by a sensor system 330. For example, payload 306 mayinclude various motion sensors (e.g., accelerometers, magnetometers,gyroscopes, and/or compasses), altimeters (e.g., pressure, sonic, orradar-based), and/or various sensors for capturing environmental data.Further, some or all of the components within payload 306 may beimplemented in a radiosonde or other probe, which may be operable tomeasure, e.g., pressure, altitude, geographical position (latitude andlongitude), temperature, relative humidity, and/or wind speed and/orwind direction, among other information.

The balloon may further include a GPS (or other positioning system)receiver 342 that may process satellite or other types of signalsreceived via the antenna system 340. The antenna system 340 may also beused to broadcast various types of signals. Further discussion relatingto receiving and broadcasting signals, particularly in connection withpositioning-related features, is provided in greater detail below.

In a further aspect, balloon 300 may be configured for altitude control.For instance, balloon 300 may include a variable buoyancy system, whichis configured to change the altitude of the balloon 300 by adjusting thevolume and/or density of the gas in the balloon 300. A variable buoyancysystem may take various forms, and may generally be any system that canchange the volume and/or density of gas in the envelope 302.

In an example embodiment, a variable buoyancy system may include abladder 310 that is located inside of envelope 302. The bladder 310could be an elastic chamber configured to hold liquid and/or gas.Alternatively, the bladder 310 need not be inside the envelope 302. Forinstance, the bladder 310 could be a ridged bladder that could bepressurized well beyond neutral pressure. The buoyancy of the balloon300 may therefore be adjusted by changing the density and/or volume ofthe gas in bladder 310. To change the density in bladder 310, balloon300 may be configured with systems and/or mechanisms for heating and/orcooling the gas in bladder 310. Further, to change the volume, balloon300 may include pumps or other features for adding gas to and/orremoving gas from bladder 310. Additionally or alternatively, to changethe volume of bladder 310, balloon 300 may include release valves orother features that are controllable to allow gas to escape from bladder310. Multiple bladders 310 could be implemented within the scope of thisdisclosure. For instance, multiple bladders could be used to improveballoon stability.

In an example embodiment, the envelope 302 could be filled with helium,hydrogen or other lighter-than-air material. The envelope 302 could thushave an associated upward buoyancy force. In such an embodiment, air inthe bladder 310 could be considered a ballast tank that may have anassociated downward ballast force. In another example embodiment, theamount of air in the bladder 310 could be changed by pumping air (e.g.,with an air compressor) into and out of the bladder 310. By adjustingthe amount of air in the bladder 310, the ballast force may becontrolled. In some embodiments, the ballast force may be used, in part,to counteract the buoyancy force and/or to provide altitude stability.

In another embodiment, a portion of the envelope 302 could be a firstcolor (e.g., black) and/or a first material from the rest of envelope302, which may have a second color (e.g., white) and/or a secondmaterial. For instance, the first color and/or first material could beconfigured to absorb a relatively larger amount of solar energy than thesecond color and/or second material. Thus, rotating the balloon suchthat the first material is facing the sun may act to heat the envelope302 as well as the gas inside the envelope 302. In this way, thebuoyancy force of the envelope 302 may increase. By rotating the balloonsuch that the second material is facing the sun, the temperature of gasinside the envelope 302 may decrease. Accordingly, the buoyancy forcemay decrease. In this manner, the buoyancy force of the balloon could beadjusted by changing the temperature/volume of gas inside the envelope302 using solar energy. In such embodiments, it is possible that abladder 310 may not be a necessary element of balloon 300. Thus, variouscontemplated embodiments, altitude control of balloon 300 could beachieved, at least in part, by adjusting the rotation of the balloonwith respect to the sun.

Further, a balloon 306 may include a navigation system (not shown). Thenavigation system may implement station-keeping functions to maintainposition within and/or move to a position in accordance with a desiredtopology. In particular, the navigation system may use altitudinal winddata to determine altitudinal adjustments that result in the windcarrying the balloon in a desired direction and/or to a desiredlocation. The altitude-control system may then make adjustments to thedensity of the balloon chamber in order to effectuate the determinedaltitudinal adjustments and cause the balloon to move laterally to thedesired direction and/or to the desired location. Alternatively, thealtitudinal adjustments may be computed by a ground-based orsatellite-based control system and communicated to the high-altitudeballoon. In other embodiments, specific balloons in a heterogeneousballoon network may be configured to compute altitudinal adjustments forother balloons and transmit the adjustment commands to those otherballoons.

As shown, the balloon 300 also includes a cut-down system 308. Thecut-down system 308 may be activated to separate the payload 306 fromthe rest of balloon 300. The cut-down system 308 could include at leasta connector, such as a balloon cord, connecting the payload 306 to theenvelope 302 and a means for severing the connector (e.g., a shearingmechanism or an explosive bolt). In an example embodiment, the ballooncord, which may be nylon, is wrapped with a nichrome wire. A currentcould be passed through the nichrome wire to heat it and melt the cord,cutting the payload 306 away from the envelope 302.

The cut-down functionality may be utilized anytime the payload needs tobe accessed on the ground, such as when it is time to remove balloon 300from a balloon network, when maintenance is due on systems withinpayload 306, and/or when power supply 326 needs to be recharged orreplaced.

In an alternative arrangement, a balloon may not include a cut-downsystem. In such an arrangement, the navigation system may be operable tonavigate the balloon to a landing location, in the event the balloonneeds to be removed from the network and/or accessed on the ground.Further, it is possible that a balloon may be self-sustaining, such thatit does not need to be accessed on the ground. In other embodiments,in-flight balloons may be serviced by specific service balloons oranother type of aerostat or aircraft.

3. Balloon Network with Optical and RF Links Between Balloons

In some embodiments, a high-altitude-balloon network may includesuper-node balloons, which communicate with one another via opticallinks, as well as sub-node balloons, which communicate with super-nodeballoons via RF links. Generally, the optical links between super-nodeballoons may be configured to have more bandwidth than the RF linksbetween super-node and sub-node balloons. As such, the super-nodeballoons may function as the backbone of the balloon network, while thesub-nodes may provide sub-networks providing access to the balloonnetwork and/or connecting the balloon network to other networks.

FIG. 4 is a simplified block diagram illustrating a balloon network thatincludes super-nodes and sub-nodes, according to an example embodiment.More specifically, FIG. 4 illustrates a portion of a balloon network 400that includes super-node balloons 410A to 410C (which may also bereferred to as “super-nodes”) and sub-node balloons 420 (which may alsobe referred to as “sub-nodes”).

Each super-node balloon 410A to 410C may include a free-space opticalcommunication system that is operable for packet-data communication withother super-node balloons. As such, super-nodes may communicate with oneanother over optical links. For example, in the illustrated embodiment,super-node 410A and super-node 401B may communicate with one anotherover optical link 402, and super-node 410A and super-node 401C maycommunicate with one another over optical link 404.

Each of the sub-node balloons 420 may include a radio-frequency (RF)communication system that is operable for packet-data communication overone or more RF air interfaces. Accordingly, each super-node balloon 410Ato 410C may include an RF communication system that is operable to routepacket data to one or more nearby sub-node balloons 420. When a sub-node420 receives packet data from a super-node 410, the sub-node 420 may useits RF communication system to route the packet data to a ground-basedstation 430 via an RF air interface. Additionally or alternatively, thesub-node may use its optical communication system to route the packetdata to a ground-based station such as via a free-space optical link orvia RF transmission. Notably, the ground-based station 430 may includeone or more of the components described above in connection with thepayload 306 of the balloon 300.

As noted above, the super-nodes 410A to 410C may be configured for bothlonger-range optical communication with other super-nodes andshorter-range RF communications with nearby sub-nodes 420. For example,super-nodes 410A to 410C may use using high-power or ultra-bright LEDsto transmit optical signals over optical links 402, 404, which mayextend for as much as 100 miles, or possibly more. Configured as such,the super-nodes 410A to 410C may be capable of optical communications atspeeds of 10 to 50 GB/sec or more.

A larger number of balloons may be configured as sub-nodes, which maycommunicate with ground-based Internet nodes at speeds on the order ofapproximately 10 MB/sec. Configured as such, the sub-nodes 420 may beconfigured to connect the super-nodes 410 to other networks and/or toclient devices.

Note that the data speeds and link distances described in the aboveexample and elsewhere herein are provided for illustrative purposes andshould not be considered limiting; other data speeds and link distancesare possible.

In some embodiments, the super-nodes 410A to 410C may function as a corenetwork, while the sub-nodes 420 function as one or more access networksto the core network. In such an embodiment, some or all of the sub-nodes420 may also function as gateways to the balloon network 400.Additionally or alternatively, some or all of ground-based stations 430may function as gateways to the balloon network 400.

4. Example Structure of a Balloon-Based Positioning System

FIG. 5 is a simplified block diagram illustrating a balloon-basedpositioning system 500, according to an example embodiment. System 500includes control system 502, ground-based station 504, a group ofballoons 506A to 506C (the group is generally designated 506), celestialobject 508, and ground-based receiver 510.

Control system 502 may include a processor and data storage, such asmemory. And the memory may take the form of or include a non-transitorycomputer-readable medium having stored thereon, instructions which canbe accessed and executed by the processor in order to carry out thefunctions described herein. Control system 502 may also have acommunication system to allow it to communicate with one or more devicessuch as ground-based station 504. In some examples, control system 502may be integrated with or may communicate with one or more other devicessuch as balloons 506A to 506C.

Ground-based station 504 may include one or more components from payload302 of balloon 300 and may provide functionality as described above.Ground-based receiver 510 may also include one or more components frompayload 302 of balloon 300 as described above. Ground-based station 510may take a variety of forms, including for example, a mobile phone, atablet or laptop computer, or a navigation system.

Throughout this disclosure, the term “ground-based” refers to anylocation on or proximate the earth's ground or surface. As such, theterm is not limited to locations that are literally on the earth'sground, but may also refer to locations in buildings or even oncommercial aircrafts. As shown in FIG. 5, in one example ground-basedstation 504 and ground-based receiver 510 may be located on the surfaceof earth 512.

Each balloon 506A to 506C may include one or more components fromballoon 300 as described above. Finally, celestial object 508 may takevarious forms, including for example a planet, a moon, or a star (e.g.,the sun).

Notably, system 500 has been provided for illustration purposes only andis not meant to be limiting. Indeed, while not necessary, someembodiments of a balloon-based positioning system may include a largenumber of balloons, including thousands, tens of thousands, or more,perhaps spanning around the entire earth Likewise, such a system mayinclude a large number of control stations, ground-based stations,celestial objects, and/or ground-based receivers.

5. Example Operation of a Balloon-Based Positioning System

FIG. 6 is a flow chart illustrating example functions of a method,according to an example embodiment. Generally, at block 602, the methodmay involve determining, by a computing device, a first set of spatialrelationships relating to a group of at least three balloons deployed inthe stratosphere. At block 604, the method may involve determining, bythe computing device, a second set of spatial relationships relating toat least a portion of the group and to a reference point. Further, atblock 606, the method may involve determining, by the computing device,a position of the reference point relative to the earth. Still further,at block 608, the method may involve using the determined first set, thedetermined second set, and the determined position of the referencepoint relative to the earth as a basis for determining a position of atarget balloon in the group relative to the earth. And at block 610, themethod may involve transmitting the determined position of the targetballoon relative to the earth. Additional details relating to thesefunctions are provided below. For illustration purposes, the functionsare described in connection with system 500. However, the functions mayalso be implemented in other systems (e.g., balloon-based positioningsystems of a larger scale).

5a) Determining a First Set of Spatial Relationships Relating to theGroup

As noted above, at block 602, the method may involve determining, by acomputing device, a first set of spatial relationships relating to agroup of at least three balloons deployed in the stratosphere. This mayinvolve control system 502 determining a first set of spatialrelationships relating to group 506. Generally, this first set ofspatial relationships defines the geometry of group 506.

The spatial relationships in the first set may take various forms. Forexample, the spatial relationships may be distance-based. As such,control system 502 determining the first set of spatial relationshipsmay involve control system 502 determining a distance between a balloonin group 506 and another balloon in group 506. As shown in FIG. 5, thismay involve control system 502 determining distance D1 between balloons506A and 506B, distance D2 between balloons 506A and 506C, and/ordistance D3 between balloons 506B and 506C.

Control system 502 may determine such distances in a variety of ways.For example, control system 502 may determine distance D1 based on the“time of flight” of a signal traveling from balloon 506A to balloon506B. This may involve several functions. A first function may involvecontrol system 502 determining a transmission time of a signal sent byballoon 506A and received by balloon 506B. In one example, balloon 506Amay encode the transmission time in the signal. Balloon 506B may thenextract the transmission time from the signal and provide it to controlsystem 502. A second function may involve control system 502 determininga receipt time of the signal by balloon 506B. In one example, balloon506B may record the time at which it receives the signal, and provide itto control system 502. A third function may involve control system 502determining a travel speed of the signal (e.g., via a look-up table).And a fourth function may involve control system 502 using thedetermined transmission time, the determined receipt time, and thedetermined travel speed as a basis for determining the distance betweenballoon 506A and balloon 506B, such as by solving for distance as afunction of time and speed. For example, control system 502 maydetermine distance D1 by determining the difference between thedetermined transmission time and the determined receipt time, andmultiplying the determined difference by the determined travel speed ofthe signal.

As another example, control system 502 may determine distance D1 basedon other distances and/or angles as shown in connection with FIG. 7.This may involve several functions. A first function may involve controlsystem 506A determining distance D4 between balloon 506A and earth 512(i.e., the center of earth 512). In one example, balloon 506A may use analtimeter to determine its altitude and provide it to control system502. Control system 502 may then determine the distance from the surfaceof earth 512 (under balloon 506A) to the center of earth 512 (e.g., viaa look-up table) and add that distance to the altitude to determinedistance D4. A second function may involve control system 502determining angle A1 between a first vector and a second vector, wherethe first vector extends from balloon 506A towards earth 512, and wherethe second vector extends from balloon 506A towards balloon 506B. Athird function may involve determining angle A2 between the secondvector and a third vector, where the third vector extends from balloon506B towards earth 512. Example ways in which such angles may bedetermined are described in greater detail below.

A fourth function may involve control system 502 using the determineddistance D4, the determined angle A1, and the determined angle A2 as abasis for determining the distance D1, such as by solving a sinefunction. Additionally or alternatively, control system 502 maydetermine distance D5 between balloon 506B and earth 512. And controlsystem 502 may use the determined distance D4, the determined distanceD5, the determined angle A1, and the determined angle A2 as a basis fordetermining distance D1, such as by solving a cosine function.

As yet another example, control system 502 may determine distance D1based on a change of an RF signal's strength between when it is receivedby a first antenna and when it is received by a second antenna, wherethe RF signal is broadcast from balloon 506A, and where both antennasextend from different portions of balloon 506B.

Additionally or alternatively to determining distance D1, control system502 may determine other distances in similar manners. For example,control system 502 may determine distance D2 and/or distance D3, andtherefore the first set of spatial relationships may include distancesD1, D2, and/or D3.

In some instances, a distance-based spatial relationship may specify adistance range between two objects. For example, if balloon 506Adetermines that it is within RF communication range of balloon 506B,balloon 506A may determine that distance D1 is within a distance rangehaving an upper limit equal to the maximum distance that an RF signalmay travel. A similar technique may also be used for balloons thatcommunicate using optical signals. Further, balloon 506A may use thereceived strength of a signal send from balloon 506B to further narrowthe range of distance D1.

Additionally or alternatively to determining a range of distance D1,control system 502 may determine other distance ranges in similarmanners. For example, control system 502 may determine a range ofdistance D2 and/or a range of distance D3, and therefore the first setof spatial relationships may include ranges of distances D1, D2, and/orD3.

The spatial relationships may also be angle-based. In one example,control system 502 determining the first set of spatial relationshipsmay involve control system 502 determining an angle between a firstvector and a second vector, where the first vector extends from a firstballoon in the group 500 towards a second balloon in the group 500, andwhere the second vector extends from the first balloon towards a thirdballoon in the group 500. As shown in FIG. 8, this may involve controlsystem 502 determining angle A3 between vectors V1 and V2.

Control system 502 determining angle A3 may involve several functions. Afirst function may involve control system 502 determining angle A4between vector V1 and a reference vector V3, where vector V3 extendsfrom balloon 506A. A second function may involve control system 502determining angle A5 between vector V2 and vector V3. A third functionmay involve control system 502 using the determined angle A4 and thedetermined angle A5, as a basis for determining angle A3. For example,where the angles A4 and A5 have different signs (relative to the vectorV3), control system 502 may determine angle A3 to be the sum of themagnitude of the angles A4 and A5. Alternatively, where the angles A4and A5 have the same signs (relative to the vector V3), control system502 may determine angle A3 to be the difference of the magnitudes of theangles A4 and A5.

Control system 502 may determine angles A4 and A5 in a variety of ways.In one example, balloon 506A may determine angle A4 and provide it tocontrol system 502. This may involve several functions. A first functionmay involve balloon 506A emitting an optical signal via a steerabletransmitter in a first position. A second function may involve balloon506A detecting a reflection of the emitted optical signal (e.g., usingan imaging system). A third function may involve responsive to detectingthe reflection of the emitted optical signal, balloon 506A determiningan offset between the first position and a second position of thesteerable transmitter, where in the second position, the steerabletransmitter is aligned with vector V3. And a fourth function may involveballoon 506A determining angle A4 using the determined offset (e.g., viaa lookup table that maps offsets to angles).

Additionally or alternatively, balloon 506A may determine angle A4 basedon the receipt of a confirmation message from balloon 506B, and balloon506A may then provide angle A4 to control system 502. This may involveseveral functions. A first function may involve balloon 506A scanningthe sky while emitting an optical signal that encodes the currentposition of the steerable transmitter. As such, balloon 506A maytransmit an optical signal via a steerable optical signal transmitter ina first position, where the optical signal includes the first position,and where the optical signal is directed at balloon 506B. In response toreceiving this signal, balloon 506B may send to balloon 506A a messageindicating that when the steerable transmitter was in the first positionballoon 506B received the optical signal. A second function maytherefore involve balloon 506A receiving the message from balloon 506B.A third function may involve responsive to balloon 506A receiving themessage, balloon 506A determining an offset between the first positionand a second position of the steerable transmitter, where in the secondposition, the steerable transmitter is aligned with the vector V3. Afourth function may involve balloon 506A determining angle A4 using thedetermined offset.

Additionally or alternatively, balloon 506A may determine angle A4 byanalyzing an image including balloon 506B. This may involve severalfunctions. A first function may involve balloon 506A using an imagingsystem to take an image of the sky. A second function may involveballoon 506A determining that balloon 506B is in the image at a firstposition. A third function may involve responsive to determining thatballoon 506B is in the image at a first position, balloon 506Adetermining an offset between the first position and a second position,where the second position represents a position in the image ofreference vector V3. A fourth function may involve balloon 506Adetermining angle A4 using the determined offset.

Notably, control system 502 may also determine angle A5 using one ormore of the techniques described above in connection with determiningangle A4. Then, after determining angles A4 and A5, control system 502may determine angle A3 as described above.

Additionally or alternatively to determining angle A3, control system502 may determine other angles related to the group 506 in similarmanners. For example, control system 502 may determine an angle betweena first vector extending from balloon 506B towards balloon 506A and asecond vector extending from balloon 506B towards balloon 506C.Likewise, control system 502 may determine an angle between a firstvector extending from balloon 506C towards balloon 506B and a secondvector extending from balloon 506C towards balloon 506A. Accordingly,the first set of spatial relationships may include one or more of suchangles.

5b) Determining a Second Set of Spatial Relationships Relating to atLeast a Portion of the Group and to a Reference Point

As noted above, at block 604, the method may involve determining, by thecomputing device, a second set of spatial relationships relating to atleast a portion of the group and to a reference point. This may involvecontrol system 502 determining a second set of spatial relationshipsrelating to at least a portion of the group 506 and to a reference pointsuch as ground-based station 504 or celestial object 508. Generally, thesecond set of spatial relationships defines the orientation of the group506 relative to earth 512.

As with those in the first set, the spatial relationships in the secondset may take various forms and may be distance-based. For example, asshown in FIG. 5, spatial relationships in the second set may includedistance D6 between balloon 506A and ground-based station 504, distanceD7 between balloon 506B and ground-based station 504, and/or distance D8between balloon 506C and ground-based station 504.

As noted above, ground-based station 504 may include one or more of thecomponents of payload 300 of balloon 300. Accordingly, control system502 may determine such distances using the similar techniques to thosedescribed above in connection with the first set of spatialrelationships. For example, control system 502 may determine the time offlight of a signal traveling from one of the balloons 506A to 506C toground-based station 504 and visa-versa. Additionally or alternatively,control system 502 may determine such distances based on a change of anRF signal's strength as described above. Also as with those in the firstset, the spatial relationships in the second set may specify a distancerange. Also, in some examples, one of balloons 506A to 502C orground-based station 504, may determine a distance or distance range andprovide it to control system 502.

Further as with those in the first set, the spatial relationships in thesecond set may be angle-based. For example, the second set may includean angle between a first vector and a second vector, where the firstvector extends from balloon 506A towards earth 512, and where the secondvector extends from balloon 506A towards celestial object 508. As shownin FIG. 9, this may involve control system 502 determining angle A6between vectors V4 and V5. In one example, balloon 506A may determineangle A6 using techniques similar to those described above in connectionwith balloon 506A determining angle A4, and provide it to control system502.

As another example, the second set may include an angle between a firstvector and a second vector, where the first vector extends fromground-based station 504 towards earth 512, and where the second vectorextends from ground-based station 504 towards balloon 506A. As shown inFIG. 10, this may involve control system 502 determining angle A7between vectors V6 and V7. In one example, ground-based station 504 maydetermine angle A7 using techniques similar to those described above inconnection with balloon 506A determining angle A4, and provide it tocontrol system 502.

As yet another example, the second set may include an angle between afirst vector and a second vector, where the first vector extends fromballoon 506A towards earth 512, and where the second vector extends fromballoon 506A towards ground-based station 504. As shown in FIG. 11, thismay involve control system 502 determining angle A8 between vectors V8and V9. In one example, balloon 506A may determine such an angle usingone or more of the techniques described above in connection with balloon506A determining angle A4, and provide it to control system 502.

5c) Determining a Position of the Reference Point Relative to the Earth

As noted above, at block 606, the method may involve determining, by thecomputing device, a position of the reference point relative to theearth. This may involve control system 502 determining a position ofground-based station 504, celestial object 508, or another objectrelative to earth 512. In one example, control system 502 may make thisdetermination by identifying the reference point and retrieving theposition of the identified reference point from a lookup table. In oneexample, balloon 506A may identify a reference point and provide it tocontrol system 502. Balloon 506A may identify a reference point in avariety of ways. For instance, where the reference point is celestialobject 508, balloon 506A may identify celestial object 508 using animaging system (e.g., that uses “star tracker” technology). Where thereference point is ground-based station 504, balloon 506A may identifythe ground-based station 504 using an imaging system and/or based on areference point identifier broadcast by ground-based station 504.

5d) Determining a Position of a Target Balloon Relative to the Earth

As noted above, at block 608, the method may involve using thedetermined first set, the determined second set, and the determinedposition of the reference point relative to the earth as a basis fordetermining a position of a target balloon in the group relative to theearth. This may involve control system 502 using the determined firstset, the determined second set, and the determined position ofground-based station 504 and/or celestial object 508 as a basis fordetermining a position of balloon 506A.

Since the determined spatial relationships inherently have at least somedegree of measurement uncertainty, in one example control system 502 mayuse the spatial relationships in the determined first set and thedetermined second set as constraint-optimization conditions inconnection with an optimization function. The optimization function mayemploy any of a variety of optimization techniques to determine (i.e.,optimize) the position of balloon 506A. Such techniques may includeminimum mean square error (MMSE), simultaneous localization and mapping(SLAM) (although without the mapping component), partially-observableMarkov design, linear quadratic estimation, dynamic Bayesian networkestimation, and/or convex optimization. In some instances,temporal-based optimization functions may also be used (i.e., that takeinto account a change in spatial relationships over time).

By using one or more of these optimization functions, control system 502may determine the most likely position of balloon 506A relative to earth512 in view of the determined first and second sets of spatialrelationships. In practice, control system 502 may determine theposition of each balloon (or at least multiple balloons) in group 506relative to earth 512 using a similar process. As such, control system502 may determine the position of balloons 506B and 506C relative toearth 512.

Control system 502 may also use balloon properties, environmentalconditions, and/or other data as constraint-optimization conditions inthis respect. For instance, in a balloon-based positioning system thatextends around the earth, the continuous or “closed-loop” nature of thegroup of balloons may be used as such a condition. This may provide abenefit that is not available in other environments in which measurementerrors may accumulate over long distances. Indeed, in such a closed-loopsystem, control system 502 may self-correct errors that would otherwiseaccumulate over such distances.

In one example, control system 502 may separately determine the positionof each balloon in group 506 relative to each other balloon in group506, and the position of group 506 relative to earth 512. As such, thefunction at block 608 may involve control system 502 using thedetermined first set as a basis for determining for each balloon ingroup 506 a position relative to the remaining balloons in group 506,and control system 502 using the determined positions relative to theremaining balloons, the determined second set, and the determinedposition of the reference point relative to earth 512 as a basis fordetermining the position of the target balloon relative to earth 512.

In some instances, control system 502 may use a first optimizationfunction to determine for each balloon in the group 506 the positionrelative to the remaining balloons in the group, and a secondoptimization function to determine the position of the target balloonrelative to the earth 512.

5e) Transmitting the Determined Position of the Target Balloon Relativeto the Earth

As noted above, at block 610, the method may involve transmitting thedetermined position of the target balloon relative to the earth. Thismay involve control system 502 transmitting the determined position ofballoon 506A relative to earth 512 to balloon 506A. In another example,control system 502 may provide the determined position to ground-basedstation 504, and ground-based station 504 may transmit the determinedposition to balloon 506A. Balloon 506A may then broadcast or otherwisetransmit the determined position and other relevant data for use byground-based receiver 510. These functions may also be performed withrespect to other balloons in the group, including for example, balloons506B and 506C.

As shown in FIG. 12, each balloon 506A to 506C may include a respectivePBM 514A to 514C configured for broadcasting (e.g., via an antenna) arespective balloon signal 516A to 516C containing balloon-positioningdata. The balloon-positioning data includes the determined position ofthe respective balloon and a corresponding time of broadcast (i.e.,indicating when the balloon signal was broadcast). Ground-based receiver510 may be configured to receive one or more of balloon signals 516A to516C and determine its position relative to earth 512 based on thecollective balloon-positioning data contained therein.

As used in this disclosure, a PBM is a functional module that refers toone or a group of components contained in the respective balloon, suchas those described in connection with FIG. 3, that may carry out thedescribed functions. For example, the PBM may include a particular setof instructions stored in the memory 314 that relate to the function ofbroadcasting a position of the respective balloon relative to the earth,together with the processor 312 for executing those instructions, andany communication systems or other associated components. However, a PBMis not limited to any particular set of components.

Notably, in some embodiments, each PBM may broadcast the respectiveballoon signal on a single channel frequency. This provides a particularadvantage over traditional positioning systems, such as the GPS, wheresatellite signals are typically broadcast simultaneously on twodifferent channel frequencies (typically L1 at 1575.42 Mhz and L2 at1227.6 Mhz) for the purpose of attempting to detect and remove delaycaused by refraction-based interference. Due to the altitude of GPSsatellites, satellite signals sent directly to ground-based receiverstraverse the ionosphere, and therefore are subject to this type ofinterference.

Since GPS satellites broadcast signals on two channel frequencies,traditional GPS receivers must be configured to receive both channelfrequencies. On the other hand, in embodiments of the balloon-basedpositioning system where balloon signals are transmitted on a singlechannel frequency, the corresponding ground-based receiver need only beconfigured to receive a single channel frequency. Among other things,this allows ground-based receivers to be less complex, and therefore,typically less expensive to produce. Notably, the single channelfrequency that is used may be any particular frequency, although inselect embodiments, it may differ from the frequencies of the L1 and L2or other commonly used frequencies to reduce or avoid potentialinterference.

Further, due to the relatively slow speed at which the balloons arelikely to travel (i.e., as compared to GPS satellites), ground-basedreceivers do not need to compensate for Doppler shifts as is the casewith GPS receivers. Again, this reduces the complexity and theproduction cost of ground-based receivers.

5f) Variations

While one or more functions of the disclosed methods have been describedas being performed by the certain entities (e.g., control system 502),the functions may be performed by any entity or combination of entities,such as those included in system 500 described above.

Also, as noted above, the disclosed system need not be limited to theconfiguration of system 500. Indeed, in practice the disclosed systemmay include thousands, tens of thousands, or even more balloons, controlsystems, ground-based stations, celestial objects, ground-basedreceivers, and/or other entities. Likewise, the method may involvedetermining thousands, tens of thousands, or even more spatialrelationships such as in the example manners described above. Notably,as more spatial relationships are determined, the control system may beable to determine the position of a target balloon with greater accuracyand with less calculation time. As such, in some embodiments, alarge-scale balloon-based positioning system may be desired.

Further, the described steps throughout this application need not beperformed in the disclosed order, although in some examples, an ordermay be preferred. Also, not all steps need to be performed to achievethe desired advantages of the disclosed systems and methods, andtherefore not all steps are required. Further, the variations describedthroughout this disclose may be applied to any of the disclosed examplesand perhaps in other environments.

Still further, the various techniques described throughout thisapplication may be utilized in environments other than a balloon-basedpositioning system. For example, the described techniques fordetermining a distance between two balloons may be used to determine thedistance between two other objects. Likewise, the described techniquesfor determining an angle between two vectors need not be utilized in thecontext of a balloon-based positioning system. Indeed, the first vectormay extend from a first object to a second object and the second vectormay extend from the first object to a reference point (e.g., a thirdobject). As such, it is contemplated that a control system (or otherdevice) may determine spatial relationships between other (non-balloon)objects. Notably, these objects may include one or more of the ballooncomponents described above, and such components may be used, at least inpart, in determining such spatial relationships. Then, based on thesespatial relationships, a control system (or other device) may determinethe position of each object relative to one or more other objects and/orrelative to a reference point such as the earth in a manner similar tothat described above in connection with the example balloon-basedpositioning systems.

6. Additional Example Advantages

In the context of the GPS, a receiver is often unable to determine itsposition because it cannot receive the signals being broadcast by one ormore of the GPS satellites. These signals may have difficulty reachingGPS receivers for a number of reasons, such as due to weak signalstrength and signal interference due to reflection, refraction, and/ormultipath propagation. In an attempt to minimize issues concerning weaksignal strength, the GPS employs a digital-sequence spread spectrum(DSSS) encoding technique that improves signal strength by utilizing anincreased amount of bandwidth. However, this technique only marginallyimproves signal strength.

As noted, GPS satellites typically orbit the earth at an altitude ofapproximately 20,000 km. As a result of the satellite signals travelingsuch a long distance, signal attenuation is often substantial, even withDSSS encoding. On the other hand, in the balloon-based positioningsystem, balloon signals sent from a balloon to a ground-based receivertravel a substantially shorter distance. In one embodiment, balloonsignals travel a distance in the range of approximately 17 km to 25 km.Further, balloon signals destined for a receiver originate beneath theionosphere, and therefore are not subject to refraction-basedinterference as discussed above. For these reasons, balloon signals arelikely to be stronger, and are more likely to reach receivers, ascompared to in a parallel GPS scenario.

Finally, when a given GPS receiver is in certain environments such ascities, tall buildings or other objects may block or interfere with thesignals. As discussed, some embodiments of the balloon-based positioningsystem may include a large number of balloons deployed across thestratosphere. Some embodiments may include thousands, tens of thousands,or even more balloons. As a result, any given ground-based receiver islikely to have a line-of-sight to many balloons, in some embodiments, asmany as 50-100 at a time. As a result, a receiver has a much greaterlikelihood of being able to receive balloon signals, as compared to forexample, a GPS receiver that may have lines-of-sight with a maximum ofapproximately eleven or twelve GPS satellites.

While various aspects and embodiments have been disclosed herein, otheraspects and embodiments will be apparent to those skilled in the art.The various aspects and embodiments disclosed herein are for purposes ofillustration and are not intended to be limiting, with the true scopeand spirit being indicated by the following claims.

What is claimed is:
 1. A method comprising: determining, by a computingdevice, a first set of spatial relationships relating to a group of atleast three balloons deployed in the stratosphere, wherein determiningthe first set comprises (i) determining a distance between a balloon inthe group and another balloon in the group, and (ii) determining anangle between a first vector and a second vector, wherein the firstvector extends from a first balloon in the group towards a secondballoon in the group, and wherein the second vector extends from thefirst balloon towards a third balloon in the group; determining, by thecomputing device, a second set of spatial relationships relating to atleast a portion of the group and to a reference point; determining, bythe computing device, a position of the reference point relative to theearth; using the determined first set, the determined second set, andthe determined position of the reference point relative to the earth asa basis for determining a position of a target balloon in the grouprelative to the earth; and transmitting the determined position of thetarget balloon relative to the earth, wherein using the determined firstset, the determined second set, and the determined position of thereference point relative to the earth as a basis for determining theposition of the target balloon relative to the earth comprises using anoptimization function to determine the position of the target balloonrelative to the earth.
 2. The method of claim 1, wherein using thedetermined first set, the determined second set, and the determinedposition of the reference point relative to the earth as a basis fordetermining the position of the target balloon relative to the earthcomprises: using the determined first set as a basis for determining foreach balloon in the group a position relative to the remaining balloonsin the group; and using the determined positions relative to theremaining balloons, the determined second set, and the determinedposition of the reference point relative to the earth as a basis fordetermining the position of the target balloon relative to the earth. 3.The method of claim 2, wherein using the determined first set as a basisfor determining for each balloon in the group the position relative tothe remaining balloons in the group comprises using a first optimizationfunction to determine for each balloon in the group the positionrelative to the remaining balloons in the group, and wherein using thedetermined positions relative to the remaining balloons, the determinedsecond set, and the determined position of the reference point relativeto the earth as a basis for determining the position of the targetballoon relative to the earth comprises using a second optimizationfunction to determine the position of the target balloon relative to theearth.
 4. The method of claim 1, wherein determining the distancebetween the balloon in the group and another balloon in the groupcomprises: determining a transmission time of a signal sent by theballoon and received by the other balloon; determining a receipt time ofthe signal by the other balloon; determining a travel speed of thesignal; and using the determined transmission time, the determinedreceipt time, and the determined travel speed as a basis for determiningthe distance between the balloon and the other balloon.
 5. The method ofclaim 1, wherein determining the distance between the balloon in thegroup and another balloon in the group comprises: determining a distancebetween the balloon and the earth; determining an angle between a thirdvector and a fourth vector, wherein the third vector extends from theballoon towards the earth, and wherein the fourth vector extends fromthe balloon towards the other balloon; determining an angle between thefourth vector and a fifth vector, wherein the fifth vector extends fromthe other balloon to the earth; and using the determined distancebetween the balloon and the earth, the determined angle between thethird vector and the fourth vector, and the determined angle between thefourth vector and the fifth vector as a basis for determining thedistance between the balloon and the other balloon.
 6. The method ofclaim 1, wherein determining the angle between the first vector and thesecond vector comprises: determining an angle between the first vectorand a third vector, wherein the third vector extends from the firstballoon; determining an angle between the second vector and the thirdvector; and using (i) the determined angle between the first vector andthe third vector and (ii) the determined angle between the second vectorand the third vector, as a basis for determining the angle between thefirst vector and the second vector.
 7. The method of claim 6, furthercomprising: the first balloon emitting an optical signal via a steerableoptical signal transmitter in a first position; the first balloondetecting a reflection of the emitted optical signal; and responsive tothe first balloon detecting the reflection of the emitted opticalsignal, the first balloon determining an offset between the firstposition and a second position of the steerable optical signaltransmitter, wherein in the second position, the steerable opticalsignal transmitter is aligned with the third vector, wherein determiningthe angle between the first vector and the third vector comprises usingthe determined offset as a basis for determining the angle between thefirst vector and the third vector.
 8. The method of claim 6, furthercomprising: the first balloon transmitting an optical signal via asteerable optical signal transmitter in a first position, wherein theoptical signal includes the first position; the first balloon receivingfrom the second balloon, a message indicating that when the steerableoptical signal transmitter was in the first position the second balloonreceived the optical signal; and responsive to the first balloonreceiving the message, the first balloon determining an offset betweenthe first position and a second position of the steerable optical signaltransmitter, wherein in the second position, the steerable opticaltransmitter is aligned with the third vector, wherein determining theangle between the first vector and the third vector comprises using thedetermined offset as a basis for determining the angle between the firstvector and the third vector.
 9. The method of claim 1, wherein thereference point comprises a celestial object, and wherein determiningthe second set comprises using an imaging system as a basis fordetermining an angle between a third vector and a fourth vector, whereinthe third vector extends from a particular balloon in the group towardsthe earth, and wherein the fourth vector extends from the particularballoon towards the celestial object.
 10. The method of claim 1, whereinthe reference point comprises a ground-based station, and whereindetermining the second set comprises determining a distance between aparticular balloon in the group and the ground-based station.
 11. Themethod of claim 1, wherein the reference point comprises a ground-basedstation, and wherein determining the second set comprises determining anangle between a third vector and a fourth vector, wherein the thirdvector extends from the ground-based station towards the earth, andwherein the fourth vector extends from the ground-based station towardsa particular balloon.
 12. The method of claim 1, further comprising: aground-based receiver receiving the transmitted position of the targetballoon relative to the earth; and the ground-based receiver using thereceived position of the target balloon relative to the earth as a basisfor determining the position of the ground-based receiver relative tothe earth.
 13. A non-transitory computer-readable medium having storedthereon program instructions that upon execution by a processor, causeperformance of a set of functions, the set of functions comprising:determining a first set of spatial relationships relating to a group ofat least three balloons deployed in the stratosphere; determining asecond set of spatial relationships relating to at least a portion ofthe group and to a reference point; determining a position of thereference point relative to the earth; using the determined first set,the determined second set, and the determined position of the referencepoint relative to the earth as a basis for determining a position of atarget balloon in the group relative to the earth; and transmitting thedetermined position of the target balloon relative to the earth, whereinusing the determined first set, the determined second set, and thedetermined position of the reference point relative to the earth as abasis for determining the position of the target balloon relative to theearth comprises using an optimization function to determine the positionof the target balloon relative to the earth.
 14. The computer-readablemedium of claim 13, wherein using the determined first set, thedetermined second set, and the determined position of the referencepoint relative to the earth as a basis for determining the position ofthe target balloon relative to the earth comprises: using the determinedfirst set as a basis for determining for each balloon in the group aposition relative to the remaining balloons in the group; and using thedetermined positions relative to the remaining balloons, the determinedsecond set, and the determined position of the reference point relativeto the earth as a basis for determining the position of the targetballoon relative to the earth.
 15. The computer-readable medium of claim14, wherein using the determined first set as a basis for determiningfor each balloon in the group the position relative to the remainingballoons in the group comprises using a first optimization function todetermine for each balloon in the group the position relative to theremaining balloons in the group, and wherein using the determinedpositions relative to the remaining balloons, the determined second set,and the determined position of the reference point relative to the earthas a basis for determining the position of the target balloon relativeto the earth comprises using a second optimization function to determinethe position of the target balloon relative to the earth.
 16. Thecomputer-readable medium of claim 13, wherein the reference pointcomprises a ground-based station or a celestial object.
 17. A systemcomprising: a group of at least three balloons deployed in thestratosphere; and a control system configured for: determining a firstset of spatial relationships relating to the group; determining a secondset of spatial relationships relating to at least a portion of the groupand to a reference point; determining a position of the reference pointrelative to the earth; using the determined first set, the determinedsecond set, and the determined position of the reference point relativeto the earth as a basis for determine a position of a target balloon inthe group relative to the earth; and transmitting the determinedposition of the target balloon relative to the earth, wherein using thedetermined first set, the determined second set, and the determinedposition of the reference point relative to the earth as a basis fordetermining the position of the target balloon relative to the earthcomprises using an optimization function to determine the position ofthe target balloon relative to the earth.
 18. The system of claim 17,wherein using the determined first set, the determined second set, andthe determined position of the reference point relative to the earth asa basis for determining the position of the target balloon relative tothe earth comprises: using the determined first set as a basis fordetermining for each balloon in the group a position relative to theremaining balloons in the group; and using the determined positionsrelative to the remaining balloons, the determined second set, and thedetermined position of the reference point relative to the earth as abasis for determining the position of the target balloon relative to theearth.
 19. The system of claim 18, wherein using the determined firstset as a basis for determining for each balloon in the group theposition relative to the remaining balloons in the group comprises usinga first optimization function to determine for each balloon in the groupthe position relative to the remaining balloons in the group, andwherein using the determined positions relative to the remainingballoons, the determined second set, and the determined position of thereference point relative to the earth as a basis for determining theposition of the target balloon relative to the earth comprises using asecond optimization function to determine the position of the targetballoon relative to the earth.
 20. The system of claim 17, furthercomprising: a ground-based receiver receiving the transmitted positionof the target balloon relative to the earth; and the ground-basedreceiver using the received position of the target balloon relative tothe earth as a basis for determining the position of the ground-basedreceiver relative to the earth.